Intellect Sharpeners.

New Zealand Herald, Volume LXIX, Issue 21130, 12 March 1932, Page 5 (Supplement)

Intellect Sharpeners.

shearing; tallies. BT T. L. BRITON. C.J.W. has sent another interesting question which occurred to him while holidaying at a friend's sheep station' in the south, last December. It-was noticeable, he states, during the shearing, that tho men "on the board always main* tained tho same ratio to one another with regard to each day's tallies, so much so that after one or two pens of shorn sheep had been counted,' the number of sheep in other pens could be determined with extraordinary nearness to the actual figures. Here is his question on the point, which the reader will find is easily answered correctly without acquiring any knowledge of mathematics beyond thai curriculum of tho sixth standard. Mr. Smith has a smallrfarm carrying fewer than one thousand sheep, and at last " shearing " all his sheep were mustered and placed in eleven different enclosures, tho same number in each. When paying off his four shearers after " cutting out,* it was found that Bill Lad shorn at. the rate of 22 sheep to Alf's 19, Charlie had shorn 60 to Bill's 55, while Fan, the " ringer " of the shed, had put through exactly 100 to Charlie's 96. This information will bo found ample to enable 1 lie reader to find, in tho manner suggested, how many sheep were shorn by tho four men.

TWO PROBLEMS. Tho two problems following may be solved without pen, or pencil. A tengallon cask contains a mixture of ale and porter in the proportion of three parts to one respectively.' The cask is not full by eight pints, and the question is how much of the mixture should be drawn off and the same quantity of porter substituted so that tho contents of the barrel will be composed of equal parts of the two k nds of liquor ? Tho second question is what is the largest sum of money in New Zealand silver currency that a person could lave in his pocket without being able to give change for a ten-shil-ling note I This question was askerl some iime ago, and after publication of the correct answer a correspondent wrote to say that he did not agree with it, submitting'an ingenious if irrelevant alternative answer by assuming something not expressed or implied in the question,which was precisely the same as now asked. There is only one correct answer. IDENTIFYING THE BROTHERS. Four brothers, whoso surnames are White, Green, Black and Grey respectively. each took his younger brother to a sports meeting, giving them upon arrival a little money to spend, the total sum then possessed by the eight of them being exactly twenty shillings, all of it in sixpences. The christain names ot tho four youngest of thfe party are each Bert, Dick, Fred and Sam, but the respective surnames are withheld, and tha puzzle, is to find them by identifying the four "pairs" of brothers, which can bo quite easily done with the additional information which follows. On their way home finances were discussed, when it was found that Bert had spent sixpence; Dick, one shilling; Fred, one and sixpence; and. Sam, two shillings. White had spent as much as his brother; Green, twice aa much as his; Black, three times as much as hii>; while Grey had spent exactly four times as much as his young brother had disbursed. The balance of the twenty shillings which they had between thera originally was then equally divided, and being; in coins all of the same value, each of the party received the same number. Can the reader find tho respective surnamos of the four youngest and thus form the eight boys into four " pairs" of brothers ?

CODE WITH VARIATION. The following sentence, consisting of seventeen words, is written in a code with one or more variations from the type frequently met, but it should not prove very difficult to find the key, though probably it nay puzzle the reader for a_ few moments to convert, it into an intelligible r,ew:> item. In the main, it is formed cn crthodox lines, but in some measure is eft the beaten-track, though the method of its construction is uniform throughout.The code should therefore not unduiy tax the patience of the would-be solver even i:i th e key may seem to be sufficiently obscurs to thoroughly test the ingenuity ol the many lovers of this class of problem. STEELHERTT DIREVEEC REFOMMIT MOTTIE ACIDETIN EAETHTRADES PEATIACREP TEELETHLISCENT HEESPRANES WORTERINE GANTSIT HA3THET FEBMINTHS TELLAMNY GENSHERRIF HESETIN SURYDASH. AVERAGES. Here are two useful questions in " averages " which tho reader will doubtless answer correctly without recourse to. •2itt.er pen or pencil, for they are purely !'or the armchair. Six boys went holidaying to one of the beaches at a recent week-end, and it cost five of them exactly hal::-a-crown each. The sixth member, Percy, was not so extravagant, for his total expenditure was fivepence less than the average expenditure of the six youngsters. How much did Percy spend? A correspondent, " L," asks the following question, which, though an old one, seems to crop up regularly in the form of a controversy concerning the correct answer. " J " and " G " are two members of a cricket team, and in a recent match 'they bowled unchanged from the first to the twentieth wicket. In the first innings the former took seven wickets for 84 runs, anc! the other three for 45. In the second innings •" J " again came out with the better average, securing two_ wickets for six against ".G's " eight for 32. Can the reader say who obtained the better average for the match, for it is understood that the trophy is still helft by the committee of the remote country club where the incident occurred, awaiting att authoritative decision on the point.

LAST WEEK'S SOLUTIONS. Art Union Speculations. —A, 25; B, 20ij C, 10; D, 15; E, 30. restoring the Figures. —Divisor, 3925; dividend, 2,559,752; and the quotient,, 652. Prices of Eggs.—Twenty at Is 3d, the same number at one penny less, and sixty at Is per dozen. Alphabetical Sum.—The respecfvo alphabetical equivalents of the digits*? 1, 2 3 4. 5, 6, 7, 8, 9 and the cipher Q are, E, U, 0, S, M, A, N, R, T and Y. Novel Code Problem.—The vowels are ! first eliminated, and also the consonants j " 0 " and " Z," leaving a reduced alphabet" of 19 letters, the alternate letters of which then give place to digits in alphahelical and numerical order tiie dicit " 1 " is substituted for " C;" 2 for "f; M 3 for "h;" 4 for " k," etc., to the. 9 for " x." The vowels are then restored and used in their normal sense. ANSWERS TO CORRESPONDENTS. " A.B.C."—Next Saturday. The matter upon which you asked for information was explained in the issue ol Januaiy 16. " Interested."— Every seventh bissextile. but this rule will nob apply M -the period includes " century years thiee of every four of which arc not leap jeais —I9OO for example. " Investor." —Upon the statement you. send St is obvious .11, at the absorbed in comm.ss.on *ndto ducted sum mentioned represents sbgb r. over 60 per cent, not m pen » E «' 6 1 S understood that deductions are made by a percentage of the turnover which isfof course, a different thing, for m tbrf. Wav the same money jeci-ed to a cut ' on eight separat#; occasions.